The 'p' position is the for powersaving mode, we throughly recommend this mode for Winter, it will dim the lights a fraction but allows them to run for longer.
Thanks for your question. Lumify DualWhite offers 4 lighting modes. The modes are 1) all lights on 2) slow flash 3) slow fade and 4) mode cycle. So I would recommend perhaps slow flash/slow flash, however these aren't exclusively a 'Twinkle mode'.
Hello there! It sounds like you're experiencing a panel fault, which is failing to register light or the lack thereof. You can purchase a replacement panel here, alternatively, get in touch (if the lights are still within warranty) and we'll be able to provide a replacement free of charge.